galileo acceleration due gravity

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Question:

Answers:Galileo Galilei performed experiments with wooden balls rolling down a highly polished inclined plane to determine that gravitational acceleration was independent of mass. There's a story that he did it by dropping various weights off the Leaning Tower of Pisa, but that's almost certainly apocryphal.

Question:What kind of information is indicated by a graph of acceleration due to gravity versus ball's mass if the slope of the curve is zero?

Answers:It is indicating that inertial mass and gravitational mass are the same property of matter.

Question:How can I measure the acceleration due to gravity by using a meter stick, stopwatch, and rubber ball? Also, what equations shoud I use?

Answers:For this particular example, no calculus is needed. However, you will need the equation of motion for a falling object:
y(t)=y0+vy0*t+(1/2)*a*t^2 where y0 is the starting height, vy0 is the initial velocity, a is the acceleration acting on the object, and t is the time elapsed.
If we drop the ball from rest vy0=0, so we're left with y(t)=y0+(1/2)*a*t^2. If we start the stopwatch as soon as we drop the ball and stop the stopwatch as soon as the ball hits the ground and t seconds have elapsed, y(t)=0.
We're left with 0=y0+(1/2)*a*t^2
We want to find a, so through the use of some algebra, we can perform the following steps:
0=y0+(1/2)*a*t^2
-y0=(1/2)*a*t^2
-2*y0=a*t^2
(-2*y0)/(t^2)=a

Question:How would you find the acceleration due to gravity at the surface of a planet if you're given:
a) mass = 1 kg
b) a graph of graviational potential energy vs. height above the surface of the planet?

Answers:POTENTIAL ENERGY IS A POINT FUNCTION defined as negative of work done by conservative force.
Here conservative force is gravitational force given by
mass * acceleration due to gravity
1 * a (say)
a newton.
If ground level is taken as zero potential then, at height h then gravitation force would have done work equal to (a) . (-h)moving it to height h (Negative because displacement and force are in opposite directions and cos 180 = -1)
Potential energy at height h would be = -W
= - (-ah)
=ah.
at any height if potential energy is known then a can be calculated using math....
(here mass = 1. So the force is equal to acceleration in magnitude)
Thus u dont need the full graph rather only a single pt is enough

From Youtube

Acceleration due to Gravity :This educational video is brought to you by Manipal K-12 Technologies formerly Edurite Technologies- a leading provider of educational content and learning solutions. This video talks about acceleration due to gravity and its values for calculations.

Acceleration Due to Gravity :In this video, I discuss the solution for a two step simple gravity acceleration problem www.mrlovescience.com